The number of silicon atoms per m3 is 5 × 1028. This is doped simultaneously with 5 × 1022 atoms per m3 of Arsenic and 5 × 1020 per m3 atoms of Indium. - Physics

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Numerical

The number of silicon atoms per m3 is 5 × 1028. This is doped simultaneously with 5 × 1022 atoms per m3 of Arsenic and 5 × 1020 per m3 atoms of Indium. Calculate the number of electrons and holes. Given that ni= 1.5 × 1016 m−3. Is the material n-type or p-type?

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Solution

Number of silicon atoms, N = 5 × 1028 atoms/m3

Number of arsenic atoms, nAs = 5 × 1022 atoms/m3

Number of indium atoms, nIn = 5 × 1020 atoms/m3

Number of thermally-generated electrons, ni = 1.5 × 1016 electrons/m3

Number of electrons, ne = 5 × 1022 − 1.5 × 1016 ≈ 4.99 × 1022

Number of holes = nh

In thermal equilibrium, the concentrations of electrons and holes in a semiconductor are related as:

nenh = ni2

`therefore "n"_"h" = ("n"_"i"^2)/"n"_"e"`

`= (1.5 xx 10^16)^2/(4.99 xx 10^22) ~~ 4.51 xx 10^9`

Therefore, the number of electrons is approximately 4.99 × 1022 and the number of holes is about 4.51 × 109. Since the number of electrons is more than the number of holes, the material is an n-type semiconductor.

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Chapter 14: Semiconductor Electronics: Materials, Devices and Simple Circuits - Exercise [Page 498]

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NCERT Physics Class 12
Chapter 14 Semiconductor Electronics: Materials, Devices and Simple Circuits
Exercise | Q 14.8 | Page 498
NCERT Physics Class 12
Chapter 14 Semiconductor Electronics: Materials, Devices and Simple Circuits
Exercise | Q 12 | Page 510

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